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Features of Hilbert Transformation to Describe the Quasi-Harmonic Oscillations with an Arbitrary Structure


G. I. Ilyin, A. G. Ilyin

Quasiharmonious fluctuations have found wide application in radio engineering. The basic sign of quasiharmonious fluctuations is that the width of his spectrum is much less, than average frequency of a spectrum. The nature of occurrence of quasiharmonious fluctuations and their structure can be various. Signals concern quasiharmonious beat-fluctuations, superposition of the harmonious components concentrated near to some average frequency, the peak-modulated fluctuations, narrow-band casual processes etc. However at research of quasiharmonious fluctuations usually isn't considered their structure and a way of realization. At researches of quasiharmonious fluctuations the greatest application was found by the model based on the theory of peak-modulated fluctuations. The specified model is put into practice in all cases without the nature and structure of real quasiharmonious fluctuation. It is obvious that in a number of almost important cases such approach can lead to considerable errors and wrong conclusions. In the real article it is shown that by consideration of quasiharmonious fluctuations with signal structure beat-fluctuations or the peak-modulated signals with suppressed bearing Hilbert's transformation leads to incorrect conclusions since Hilbert's transformation is linear only in a case when bending around quasiharmonious fluctuations isn't sign-variable function. The technique of correct use of transformation of Hilbert for consideration of quasiharmonious fluctuations with any structure is offered.

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